$C=105+\frac{7}{24} m$ $\newline$ A nutritionist uses the given equation as a measure of the total Calories, $C$ , in a half bagel covered in $m$ grams of cream cheese. What is the best interpretation of $24$ as shown in the equation? $\newline$ Choose $1$ answer: $\newline$ (A) A half bagel with no cream cheese has $24$ Calories. $\newline$ (B) A half bagel and $24$ grams of cream cheese have the same number of Calories. $\newline$ (C) The number of Calories increases by $24$ for every additional $7$ grams of cream cheese. $\newline$ (D) The number of grams of cream cheese increases by $24$ for every additional $7$ Calories.

Full solution

C=105+\frac{7}{24} m

\newline

A nutritionist uses the given equation as a measure of the total Calories,

C

, in a half bagel covered in

m

grams of cream cheese. What is the best interpretation of

24

as shown in the equation?

\newline

Choose

1

answer:

\newline

(A) A half bagel with no cream cheese has

24

Calories.

\newline

(B) A half bagel and

24

grams of cream cheese have the same number of Calories.

\newline

24

for every additional

7

grams of cream cheese.

\newline

(D) The number of grams of cream cheese increases by

24

for every additional

7

Calories.

Identify Components: The equation is $C = 105 + \left(\frac{7}{24}\right)m$ . Let's identify the components of the equation.
Constant $105$ : The constant $105$ represents the Calories in a half bagel without cream cheese.
Fraction $(\frac{7}{24}):</b> The fraction \$(\frac{7}{24})$ is the rate at which Calories increase per gram of cream cheese added.
Variable $m$ : The variable $m$ represents the grams of cream cheese.
Denominator $24$ : The number $24$ in the denominator of the fraction $(\frac{7}{24})$ indicates how many grams of cream cheese are needed for an increase of $7$ Calories.
Calories Increase Explanation: So, for every $24$ grams of cream cheese added, the total Calories increase by $7$ .
Incorrect Option Explanation: This means that option (C) ＂The number of Calories increases by $24$ for every additional $7$ grams of cream cheese＂ is incorrect because it's the other way around.